Well, these topics are like conversations, and some drift does happen. I've been chastised by one of the mods for mentioning this topic in other forums. In my own days as a moderator (many moons ago and not here), I did the exact same thing.
But to get back on topic, I actually have several scenarios where Harry could have gotten that hollow pip, and it would have made sense within the context of the story. Because no one likes walls of text, I'll post it in pieces... let's start with early Voyager...the first couple of seasons might not be ideal, but given that Harry was doing lieutenant work from the outset, not entirely inappropriate, either...
1. FACES - Pete Durst was a lieutenant in the Operations division, and presumably Harry's immediate superior. When he died, there was presumably no lieutenant in operations. Assuming there really is a command structure (whatever that is), said lieutenant would need to be replaced. Since Voyager can't exactly comm Starfleet and ask them to send out a new one, promoting from within (also known as a "battlefield promotion") is the only solution. No one likes to rank up that way, especially if the dead superior is a friend and colleague, but you can resolve to honor their memory by doing the job as well as you can.
2. TWISTED - Janeway mentions that Harry was a bright spot in the mission, the way she did in the actual episode, but she simply doesn't leave it at that. Instead, she reveals that she intends to put him up for promotion to lieutenant as soon as the affair is over. This follows directly on the heels of his imminent promotion in the alternative reality of "Non Sequiteur", the immediately previous episode. Harry has his higher rank when he shows up in "Parturition", and since it's been discussed in two episodes, neither a ceremony nor further discussion is necessary.
3. RESOLUTIONS - For most of the series, Harry is a mature, capable, and professional officer. But, because they needed to show how upset the crew was about Janeway being gone, the writers decided that their only option was a spot of character assassination, so Harry basically behaved like a nine-year-old who didn't get his way. But, what if said writers had chosen differently? What if he had simply suggested contacting the Vidiians (they were right there), but pulled back when Tuvok didn't buy into his sophistry? There would have been other ways to show how upset the crew was (and maybe they would have shown that everyone was upset, not just one person), and Kes would still have been able to bring Tuvok around. Meanwhile, the latter could have acted like he was really taking command: he puts on the correct uniform and rank insignia, Ayala is bumped up to security chief (they might have to let him talk again), and Tom is revealed to have a new appreciation for Chakotay due to his elevation to acting first officer. In the same process, Harry receives a field promotion to lieutenant. When Janeway and Chakotay have been safely retrieved and are carefully talking pure shop at episode's end, Janeway could simply state that Harry was due anyway, and she'll let his promotion stand.
